A thermo-mechanical three-dimensional finite element model is developed for use in determining the temperature history and residual stress in a Cu-H13 thin wall plate deposited by means of the laser engineered net shaping process. The same model is also applied to an H13-H13 sample in order to compare the results. The input laser power is adjusted for each layer and three different scanning speeds so as to maintain a steady molten pool size and a predefined pool depth of one and a half layers in thickness. It is observed that for a constant scanning speed, the required laser power decreases with the addition of more layers, and with an increase in the scanning speed the laser power needs to be increased. During the deposition of the first two layers, the required input laser power is significantly higher for the H13-H13 sample than for the Cu-H13 one because of the high heat conduction rate through the Cu substrate. The z-component (growth direction) of the residual stresses is found to be dominant over the other components and is compressive near the center of the wall and tensile at the free edges, which is consistent with the experimental results presented in the literature. The residual stress levels near the free edges are found to be higher in the Cu-H13 sample than in the H13-H13 sample. In these regions, the unidirectional scanning strategy results in a higher stress accumulation than the alternative scanning strategy.